The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in the Homework assignments page will always be accurate.
| Wk | Lectures | Sections in Text | Topics |
|---|---|---|---|
| 1 | 6/23 | Presentation of the course | |
| 6/24 | Chap.2 | Composition laws | |
| 2 | 6/27 | Chap.3, Chap.4 | Groups |
| 6/29 | Chap.5 | Subgroups | |
| 7/01 | Chap.5 | Generators, cyclic groups | 3 | 7/06 | Chap.6 | Functions |
| 7/07 | Complements on subgroups, discussion of Quiz 1 (solution) | ||
| 7/08 | Chap.7 | Bijections | 4 | 7/11 | Chap.12, Chap.14 | Equivalence relations, homomorphisms |
| 7/13 | Chap. 15 | Cosets, normal subgroups, quotient groups | |
| 7/14 | Chap.7 | More on quotients | 7/15 | Chap.16 | The First Isomorphism Theorem | 5 | 7/18 | Chap.8 | Symmetric groups (Prof. Tanabe) |
| 7/20 | Chap. 11 | Cyclic groups and their subgroups - Review session (Prof. Muetzel) | |
| 7/21 | Midterm Exam | Solution | 7/22 | Chap. 13 | Lagrange's Theorem and application (S. Chari) | 6 | 7/25 | More on the order and index of subgroups |
| 7/27 | Chap. 8 | The alternating group | |
| 7/28 | Wrap-up discussion on groups | 7/29 | Chap. 17 | Rings | 7 | 8/01 | Chap. 18 | Morphisms and ideals |
| 8/03 | Chap. 18 | Properties of ideals | |
| 8/04 | Discussion on rings | 8/05 | Chap. 19 | Quotient rings, fields | 8 | 8/08 | Chap. 20 | Fields of fractions, complex numbers |
| 8/10 | Chap. 22, Chap. 24 | Arithmetic in $\mathbb{Z}$ and $F[X]$ | |
| 8/11 | Complements and discussion on rings | 8/12 | Chap. 22, Chap. 25 | Factorization in $\mathbb{Z}$ and $F[X]$ | 9 | 8/15 | Chap. 26 | Irreducibility in polynomial rings |
| 8/17 | Chap. 27 | Fields extensions | |
| 8/18 | Quiz 2 (solution) | 8/19 | Chap. 28, Chap. 29 | Degrees of fields extensions | 10 | 8/22 | Wrap-up |
| 8/24 | Chap. 30 | Application: ruler and compass constructions | 8/29 | Final Examination | due by noon (solution) |